Around the Internet, on TV talk shows and in some fitness centers, people are touting a new weight-loss trend – the Paleolithic diet. Proponents suggest the modern Stone Age nutrition plan mirrors the diet on which humans evolved over millions of years. Adherents swear off farmed foods like wheat, dairy, sugar and legumes and rely on a hunter-gatherer menu of meat, nuts, fruit and vegetables.

“The Paleo Diet is a lifestyle based on the idea that in the past 40,000 years, our DNA has changed very little,” says the Dr. Oz Show website. “Therefore, eating processed foods like cereals, dairy products, and refined sugars invite disease and weight...